Which of the following is a quadratic equation?
(a) $(x^{2} + 1) = (2 - x)^{2} + 3$
(b) $x^{3} - x^{2} = (x - 1)^{3}$
(c) $2 x^{2} + 3 = (5 + x) (2 x - 3)$
(d) None of these

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Solution

(b) $x^{3} - x^{2} = (x - 1)^{3}$

$∵ x^{3} - x^{2} = {(x - 1)}^{3} ⇒ x^{3} - x^{2} = x^{3} - 3 x^{2} + 3 x - 1 ⇒ 2 x^{2} - 3 x + 1 = 0, which is a quadratic equation$

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Q. Question 1
Which of the following is a quadratic equation?
(a)

x^{2} + 2 x + 1 = (4 - x)^{2} + 3

(b)

- 2 x^{2} = (5 - x) (2 x - \frac{2}{5})

(c)

(k + 1) x^{2} + \frac{3}{2} x = 7, w h e r e k - = - 1

(d)

x^{3} - x^{2} = (x - 1)^{3}

Question 1
Which of the following is a quadratic equation?
(a) $x^{2} + 2 x + 1 = (4 - x)^{2} + 3$
(b) $- 2 x^{2} = (5 - x) (2 x - \frac{2}{5})$
(c) $(k + 1) x^{2} + \frac{3}{2} x = 7, w h e r e k = - 1$
(d) $x^{3} - x^{2} = (x - 1)^{3}$

Which of the following is not a quadratic equation?
(a) $3 x - x^{2} = x^{2} + 5$
(b) $(x + 2)^{2} = 2 (x^{2} - 5)$
(c) $(2 x + 3)^{2} = 2 x^{2} + 6$
(d) $(x - 1)^{2} = 3 x^{2} + x - 2$

Q. Which of the following is a quadratic equation?
(a)

x^{2} - 3 \sqrt{x} + 2 = 0

(b)

x + \frac{1}{x} = x^{2}

(c)

x^{2} + \frac{1}{x^{2}} = 5

(d)

2 x^{2} - 5 x = (x - 1)^{2}

Question 2
Which of the following is not a quadratic equation?
(a) $2 (x - 1)^{2} = 4 x^{2} - 2 x + 1$
(b) $2 x - x^{2} = x^{2} + 5$
(c) ${(\sqrt{2} x + \sqrt{3})}^{2} = 3 x^{2} - 5 x$
(d) $(x^{2} + 2 x)^{2} = x^{4} + 3 + 4 x^{3}$

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Which of the following is a quadratic equation? (a) (x2+1)=(2-x)2+3 (b) x3-x2=(x-1)3 (c) 2x2+3=(5+x)(2x-3) (d) None of these

(b) x3 - x2 = (x - 1)3 ∵ x3 − x2 = (x − 1)3⇒ x3 − x2 = x3 − 3x2 + 3x − 1⇒ 2x2 − 3x + 1 = 0, which is a quadratic equation

Which of the following is a quadratic equation?
(a) $(x^{2} + 1) = (2 - x)^{2} + 3$
(b) $x^{3} - x^{2} = (x - 1)^{3}$
(c) $2 x^{2} + 3 = (5 + x) (2 x - 3)$
(d) None of these

(b) $x^{3} - x^{2} = (x - 1)^{3}$

$∵ x^{3} - x^{2} = {(x - 1)}^{3} ⇒ x^{3} - x^{2} = x^{3} - 3 x^{2} + 3 x - 1 ⇒ 2 x^{2} - 3 x + 1 = 0, which is a quadratic equation$